The proposed research aims at: a) Improving the curent knowledge about the linkage map, by testing for new markers, blood samples from 2,000 families extensively typed for other genetic markers under previous NIH grants. Large numbers of posssible linkages will then be available for testing with comparatively little new laboratory work and expense. b) Improving the understanding of the genetics of inherited diseases with unclear mode of transmission by using as markers alleles at well-defined loci. This will be done by formal mathematical analysis of genetic patterns taking into consideration information about biases incurred in the selection of families studied, associations between marker alleles and the disease in question and compatibility of data with particular genetic models of disease. The possibility of, and reasons for, heterogeneity in these diseases will be explored in an attempt to separate genetic from non-genetic causes. Data on insulin dependent diabetes mellitus (IDDM), from our own studies and those of others in the literature, will be used as the empirical control of the models to be developed. We shall continue to devise appropriate methods for defining linkage in the presence of population association between a disease and specific alleles at a (possibly)linked locus. We shall continue to clarify the characteristics of the "haplotype relative risk" (HRR) statistic, proposed by us to replace the "relative risk" (RR) of Woolf in order to eliminate the effect of heterogeneity between samples of patients and controls. As a result of the advances expected from this work, we should be able to define the linkage relationships of several "new" polymorphic traits with the 25 "old" ones already defined in our sample and among themselves. We also expect to use the new mathematical tools to be developed for the study of diseases of complex genetics, such as IDDM, with a view to increasing the precision of genetic counselling and, more importantly, to suggesting approaches for the study of the mechanisms involved.